A U.S. independent monitor said HSBC Holdings PLC is moving too slowly to fix some of its compliance problems, a tough assessment that comes as the bank is grappling with other issues, including allegations it aided tax evasion.

The monitor’s report, summarized in a court filing Wednesday, comes as the bank has spent handsomely and hired thousands of staffers in an effort to overhaul its controls in the wake of a $1.9 billion...